Question: Simplify the following expression: $ n = \dfrac{q + 1}{q + 2} - 7 $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the second expression by $\dfrac{q + 2}{q + 2}$ $ \dfrac{7}{1} \times \dfrac{q + 2}{q + 2} = \dfrac{7q + 14}{q + 2} $ Therefore $ n = \dfrac{q + 1}{q + 2} - \dfrac{7q + 14}{q + 2} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{q + 1 - (7q + 14) }{q + 2} $ Distribute the negative sign: $n = \dfrac{q + 1 - 7q - 14}{q + 2}$ $n = \dfrac{-6q - 13}{q + 2}$